The Indo-Canadian combo notched up a facile 6-0 6-1 win over Australian pair of Jessica Moore and Matt Reid in the opening match that lasted just 39 minutes.
The seeded seventh duo will next face New Zealand's Artem Sitak and Elina Svitolina of Ukraine.
Bopanna and Dabrowski send down as many as five aces and converted five break points out of the seven chances that came their way.
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